The field of the invention is systems and methods for electrical properties tomography (“EPT”). More particularly, the invention relates to systems and methods for EPT using magnetic resonance imaging (“MRI”).
Electrical properties of biological tissues, which include of electrical conductivity and permittivity, depend on the frequency of external electromagnetic fields. The electrical properties also vary as a function of the relative intracellular and extracellular fluid volumes, the ionic concentrations, and the cellular membrane permeability. Both electrical conductivity and permittivity can be affected by various pathological conditions. For instance, ex vivo experimental results have shown that cancerous tissues have significantly different electrical property values—over a wide electromagnetic frequency spectrum—compared to normal tissues. Examples include differences of more than 200 percent for breast cancer and more than 100 percent for bladder cancer at radio frequencies and microwave frequencies. It is therefore anticipated that electrical property imaging is able to provide important information for cancer diagnosis and monitoring disease progression.
In the past decades, a number of efforts have been made in an attempt to map electrical property distributions in vivo. Recently, electrical properties tomography (“EPT”) has gained considerable interest as a non-invasive, in vivo imaging approach to simultaneously map conductivity and permittivity at the Larmor frequency of protons using MRI scanners. Compared with the related technique, electrical impedance tomography (“EIT”), EPT provides significantly higher spatial resolution, does not require electrode mounting or current injection, and is not hampered by shielding effects due to non-conductive media. Although magnetic resonance electrical impedance tomography (“MREIT”) has been developed to address the low spatial resolution of EIT, it still needs considerable amount of current to be injected into the object, which can be harmful for in vivo applications, and also suffers from the shielding effects noted above.
In addition to their value for assessing tissue pathology, electrical property values at the operating Larmor frequency are a key factor in quantifying local specific absorption rate (“SAR”). At high (3T) and ultra-high (≥7T) field magnetic field strengths, SAR poses a safety concern in MRI examinations and becomes a significant limiting factor in MRI applications. Knowing electrical property distributions could help deduce the applied radio frequency (“RF”) electric fields and allow for fast, subject-specific SAR estimation. Using this SAR information as a constraint to design RF pulses could enhance flexible management of tissue heating and could optimize the RF excitation efficacy, which in turn would contribute to further optimizing the use of high-field and ultra-high-field MRI scanners. The practical use of these high-field and ultra-high-filed MRI scanners would make the intrinsically higher signal-to-noise ratio (“SNR”) and contrast-to-noise ratios (“CNR”) obtained with these systems available to routine clinical use.
The concept of imaging electrical properties based on measured magnetic resonance signals was introduced by E. M. Haacke, et al., in “Extraction of conductivity and permittivity using magnetic resonance imaging,” Phys. Med. Biol., 1991; 36:723-734. In that work, the authors suggested that as the field strength increases, the RF wavelength reduces to be on the order of the body size, distortions of the B1 fields occur inside the sample, from which the electrical properties could be estimated. H. Wen later pointed out in “Noninvasive quantitative mapping of conductivity and dielectric distributions using RF wave propagation effects in high-field MRI,” Proc. SPIE 5030, Medical Imaging 2003: Physics of Medical Imaging, 471-477, that the perturbation of the RF field in high-field MRI directly relates with the conductivity and permittivity distribution in the sample, and could be explained by an electromagnetic wave equation—the homogeneous Helmholtz equation. From then on, this equation has been utilized in the majority of EPT studies.
Biological tissues may exhibit rapid spatial changes in electrical properties due to their complicated structures. Such rapid spatial variation in electrical properties has been a challenge to existing EPT approaches as most of them are based upon the homogenous formula. Derived from Maxwell's equations, several algorithms trying to tackle the boundary issue have been proposed, either based on the inhomogeneous Helmholtz equations or utilizing the continuous nature of Gauss's Law for magnetism. However, in vivo applications reported so far making use of these algorithms often result in EP maps suffering inconstant fidelity and fairly large variance, due to either high computational demands of the numerical solution or the inherently high sensitivity of such EPT algorithms to measurement noise.
In light of the foregoing, there remains a need to provide a reliable method for performing EPT in the presence of noise and for inhomogeneous media, especially at boundaries between biological tissues having different electrical property characteristics.